The receiver must know when each symbol starts (timing), what the carrier phase is (carrier recovery), and roughly what the transmit oscillator's frequency is (frequency offset). Without these, the matched filter samples at the wrong instant or rotates the constellation into uselessness.
8.1 Carrier recovery
Two main approaches.
- Pilot-aided. The transmitter inserts a known reference signal (pilot tone, preamble). The receiver locks a phase-locked loop (PLL) to the pilot. GPS, OFDM, and most modern systems do this.
- Decision-directed. A Costas loop uses two PLLs in quadrature. After demodulation, the I and Q outputs are multiplied to produce an error signal proportional to phase error; the error drives the local oscillator. Costas loops are the standard for BPSK and QPSK carrier recovery without a pilot.
8.2 Symbol timing recovery
Two textbook techniques:
- Early-late gate. Two correlators integrate a slightly-early and a slightly-late version of the matched filter output. The difference of their magnitudes drives a timing-error signal that adjusts the local symbol clock. Simple, robust, used in many digital receivers.
- Gardner detector. Computes a timing error from products of consecutive received samples; works at two samples per symbol; widely used in digital modems and DVB receivers.
Sampling slightly before or after the optimum point loses SNR rapidly. At BER , a timing error of 10% of the symbol period can cost 1 dB.
8.3 Frame synchronization
Above the symbol layer, the receiver also needs to know where frames begin. A unique known preamble (e.g., the 11-bit Barker sequence at the head of every Wi-Fi frame, or the 0x47 sync byte at the start of every MPEG-TS packet) is correlated against to declare frame start. The same Chapter 3 cross-correlation idea, again.